Abstract
Harmonic oscillator states have played an important role in nuclear structure. This has encouraged nuclear physicists to develop elaborate mathematical techniques, based on group theory, for dealing with n-particle states in the harmonic oscillator (ho) potential. The n-particle ho states are used in this article to represent the electronic wavefunctions. The matrix elements of the physical Hamiltonians with respect to the n-particle ho states are explicitly evaluated. Applications to atoms and diatomic molecules of up to four electrons are given as well as a discussion of H3+. An analysis for closed shells in the ho potential, where the matrix elements can be reduced to those of one or two particles, is also given. The validity of the approximations involved and the possibilities of the method are discussed critically.
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